Magnetic field measurement apparatus, magnetic field measurement method, and storage medium with magnetic field measurement program stored thereon

ABSTRACT

A magnetic field measurement apparatus including a magnetic sensor array having magnetic sensor cells capable of detecting magnetic fields in three axial directions arranged in three dimensions, each magnetic sensor cell including a plurality of magnetic sensors that each have a magnetoresistive element and a magnetic flux concentrator arranged at least at one of one end and another end of the magnetoresistive element; AD converters that respectively convert analog detection signals output by the magnetic sensors into digital measurement data; a magnetic field acquiring section that acquires the digital measurement data; a calibration computing section that calibrates the digital measurement data from the magnetic field acquiring section, using at least one of a main-axis sensitivity, cross-axis sensitivities, and an offset; and a gradient magnetic field computing section that calculates a gradient magnetic field using magnetic field measurement data resulting from the calibration of the digital measurement data.

The contents of the following Japanese patent application(s) areincorporated herein by reference:

2018-110417 filed in JP on Jun. 8, 2018

2019-075742 filed in JP on Apr. 11, 2019

BACKGROUND 1. Technical Field

The present invention relates to a magnetic field measurement apparatus,a magnetic field measurement method, and a storage medium with amagnetic field measurement program stored thereon.

2. Related Art

A conventional biomagnetic field measurement apparatus is known thatuses a fluxmeter in which superconducting quantum interference devices(SQUIDs) are arranged in a two-dimensional array, as shown in PatentDocument 1, for example.

-   Patent Document 1: Japanese Patent Application Publication No.    2008-142154

A conventional fluxmeter is configured to measure either a magneticfield component in a Z direction perpendicular to an XY plane orientedsubstantially along a body surface of a biomagnetic field generated froma living body, or a magnetic field component in the X direction and amagnetic field component in the Y direction. However, in order to moreaccurately examine a living body, a magnetic field measurement apparatusis desired that can obtain a more detailed gradient magnetic fielddistribution.

SUMMARY

In order to solve the above problem, according to a first aspect of thepresent invention, provided is a magnetic field measurement apparatus.The magnetic field measurement apparatus may comprise a magnetic sensorarray having a plurality of magnetic sensor cells capable of detectingmagnetic fields in three axial directions arranged in three dimensions,each magnetic sensor cell including a plurality of magnetic sensors thateach have a magnetoresistive element and a magnetic flux concentratorarranged at least at one of one end and another end of themagnetoresistive element. The magnetic field measurement apparatus maycomprise a plurality of AD converters that respectively convert analogdetection signals output by the plurality of magnetic sensors intodigital measurement data. The magnetic field measurement apparatus maycomprise a magnetic field acquiring section that acquires the digitalmeasurement data. The magnetic field measurement apparatus may comprisea calibration computing section that calibrates the digital measurementdata from the magnetic field acquiring section, using at least one of amain-axis sensitivity, cross-axis sensitivities, and an offset. Themagnetic field measurement apparatus may comprise a gradient magneticfield computing section that calculates a gradient magnetic field usingmagnetic field measurement data resulting from the calibration of thedigital measurement data. The gradient magnetic field computing sectionmay calculate the gradient magnetic field in three dimensions formagnetic fields in all three axial directions, by calculating adifference in magnetic fields between adjacent magnetic sensor cellsamong the plurality of magnetic sensor cells, using the magnetic fieldmeasurement data measured between the adjacent magnetic sensor cells.

The three axial directions and directions in which of the threedimensions the magnetic sensor cells are arranged may be the same.

The gradient magnetic field computing section may calculate the gradientmagnetic field that is second-order or higher, using the measurementdata measured between a plurality of pairs of the adjacent magneticsensor cells.

The gradient magnetic field computing section may calculate a differencein the magnetic fields between the adjacent magnetic sensor cells, usingthe measurement data measured between the adjacent magnetic sensorcells.

The plurality of magnetic sensor cells may each include a plurality ofsensor sections that each include the magnetic sensor and a coil. Theplurality of sensor sections may be arranged in a manner to not overlapwith each other when viewed from each of the three dimensionaldirections.

The plurality of sensor sections may each be arranged such that one endis provided at a gap located between the plurality of sensor sectionsand another end extends away from the gap in a corresponding axialdirection among the three axial directions.

The magnetic field measurement apparatus may further comprise amalfunction determining section that determines a malfunction of themagnetic sensor array, based on the gradient magnetic field calculatedby the gradient magnetic field computing section.

The malfunction determining section may calculate a value indicatingrotation of the magnetic field at a position of any magnetic sensor cellamong the plurality of magnetic sensor cells, based on the gradientmagnetic field, and determine that the magnetic sensor array ismalfunctioning if the value indicating the rotation of the magneticfield is greater than or equal to a first threshold value.

The malfunction determining section may calculate a value indicatingdivergence of the magnetic field at a position of any magnetic sensorcell among the plurality of magnetic sensor cells, based on the gradientmagnetic field, and determine that the magnetic sensor array ismalfunctioning if the value indicating the divergence of the magneticfield is greater than or equal to a second threshold value.

The calibration computing section may perform a computation to alignorientations of the plurality of magnetic sensor cells.

According to a second aspect of the present invention, provided is amagnetic field measurement method for measuring a magnetic field with amagnetic field measurement apparatus. The magnetic field measurementmethod may comprise converting, with the magnetic field measurementapparatus, analog detection signals output respectively by a pluralityof magnetic sensors, in a magnetic sensor array having a plurality ofmagnetic sensor cells capable of detecting magnetic fields in threeaxial directions arranged in three dimensions, with each magnetic sensorcell including a plurality of the magnetic sensors that each have amagnetoresistive element and a magnetic flux concentrator arranged atleast at one of one end and another end of the magnetoresistive element,into digital measurement data. The magnetic field measurement method maycomprise acquiring the digital measurement data. The magnetic fieldmeasurement method may comprise calibrating the digital measurement datausing at least one of a main-axis sensitivity, cross-axis sensitivities,and an offset. The magnetic field measurement method may comprisecalculating a gradient magnetic field using magnetic field measurementdata resulting from the calibration of the digital measurement data. Thecalculating the gradient magnetic field may include calculating thegradient magnetic field in three dimensions for magnetic fields in allthree axial directions, by calculating a difference in magnetic fieldsbetween adjacent magnetic sensor cells among the plurality of magneticsensor cells, using the magnetic field measurement data measured betweenthe adjacent magnetic sensor cells.

According to a third aspect of the present invention, provided is astorage medium storing thereon a magnetic field measurement program. Themagnetic field measurement program may be executed by a computer. Themagnetic field measurement program may cause the computer to function asa plurality of AD converters that respectively convert analog detectionsignals output by a plurality of magnetic sensors into digitalmeasurement data, the plurality of magnetic sensors being in a magneticsensor array having a plurality of magnetic sensor cells capable ofdetecting magnetic fields in three axial directions arranged in threedimensions, each magnetic sensor cell including a plurality of themagnetic sensors that each have a magnetoresistive element and amagnetic flux concentrator arranged at least at one of one end andanother end of the magnetoresistive element. The magnetic fieldmeasurement program may cause the computer to function as a magneticfield acquiring section that acquires the digital measurement data. Themagnetic field measurement program may cause the computer to function asa calibration computing section that calibrates the digital measurementdata from the magnetic field acquiring section, using at least one of amain-axis sensitivity, cross-axis sensitivities, and an offset. Themagnetic field measurement program may cause the computer to function asa gradient magnetic field computing section that calculates a gradientmagnetic field using magnetic field measurement data resulting from thecalibration of the digital measurement data, and that calculates thegradient magnetic field in three dimensions for magnetic fields in allthree axial directions, by calculating a difference in magnetic fieldsbetween adjacent magnetic sensor cells among the plurality of magneticsensor cells, using the magnetic field measurement data measured betweenthe adjacent magnetic sensor cells.

The summary clause does not necessarily describe all necessary featuresof the embodiments of the present invention. The present invention mayalso be a sub-combination of the features described above.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a configuration of a magnetic field measurement apparatus10 according to the present embodiment.

FIG. 2 shows a configuration of the magnetic sensor unit 110 accordingto the present embodiment.

FIG. 3 shows a configuration and arrangement of the magnetic sensorcells 220 in the magnetic sensor array 210 according to the presentembodiment.

FIG. 4 shows an example of input/output characteristics of a magneticsensor of a magnetoresistive element according to the presentembodiment.

FIG. 5 shows an example of a configuration of a sensor section 300according to the present embodiment.

FIG. 6 shows an example of an input/output characteristic of a sensorsection 300 according to the present embodiment.

FIG. 7 shows an example of a configuration of a magnetic sensor 520according to the present embodiment.

FIG. 8 shows a configuration of the magnetic sensor array 210, thesensor data collecting section 230, and a sensor data processing section800 according to the present embodiment.

FIG. 9 shows a flow for calculating an Nth-order gradient magneticfield, according to the present embodiment.

FIG. 10 shows an example of a first-order gradient magnetic fielddistribution obtained by the magnetic field measurement apparatus 10according to the present embodiment.

FIG. 11 shows an example of a second-order gradient magnetic fielddistribution obtained by the magnetic field measurement apparatus 10according to the present embodiment.

FIG. 12 shows a configuration of the magnetic sensor array 210, thesensor data collecting section 230, the sensor data processing section800, and a malfunction determining section 1200 according to amodification of the magnetic field measurement apparatus 10.

FIG. 13 shows a malfunction determination flow according to the presentembodiment.

FIG. 14 shows a modification of the magnetic sensor cells 220 in themagnetic sensor array 210 according to the present embodiment.

FIG. 15 shows an example of a computer 2200 in which aspects of thepresent invention may be wholly or partly embodied.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, some embodiments of the present invention will bedescribed. The embodiments do not limit the invention according to theclaims, and all the combinations of the features described in theembodiments are not necessarily essential to means provided by aspectsof the invention.

FIG. 1 shows a configuration of a magnetic field measurement apparatus10 according to the present embodiment. The magnetic field measurementapparatus 10 measures a magnetic field using a magnetoresistive element.The magnetic field measurement apparatus 10 is an example of amagnetocardiography measurement apparatus, and measures the magneticfield generated by the electrical activity of a human heart (referred toas a “heart magnetic field”). Instead, the magnetic field measurementapparatus 10 may be used to measure the heart magnetism of a living bodythat is not human, or to measure biomagnetic fields other than a heartmagnetic field, such as a brain magnetic field. Furthermore, themagnetic field measurement apparatus 10 may be used for magnetic flawexaminations to detect flaws or the like on or below the surface ofsteel material or welded portions.

The magnetic field measurement apparatus 10 includes a body portion 100and an information processing section 150. The body portion 100 is acomponent for sensing the heart magnetism of a subject, and includes amagnetic sensor unit 110, a head 120, a drive section 125, a baseportion 130, and a pole portion 140.

The magnetic sensor unit 110 is arranged at a position facing the hearton the chest of the subject when measuring the heart magnetism, andsenses the heart magnetism of the subject. The head 120 supports themagnetic sensor unit 110, and causes the magnetic sensor unit 110 toface the subject. The drive section 125 is provided between the magneticsensor unit 110 and the head 120, and changes the orientation of themagnetic sensor unit 110 relative to the head 120 when calibration isperformed. The drive section 125 according to the present embodimentincludes a first actuator that can rotate the magnetic sensor unit 110by 360 degrees on the Z-axis in the drawing and a second actuator thatrotates the magnetic sensor unit 110 on an axis perpendicular to theZ-axis (the X-axis in the state shown in the drawing), and the drivesection 125 uses these actuators to change the azimuth angle and zenithangle of the magnetic sensor unit 110. Here, for example, the azimuthangle of the magnetic sensor unit 110 may be an angle by which a planeof the magnetic sensor unit 110 rotates about an axis (the Z axis in thefigure) coinciding with the direction of zenith which is defined as thedirection pointing to the chest of a subject, and the zenith angle ofthe magnetic sensor unit 110 may be an angle that the plane of themagnetic sensor unit 110 forms with the axis coinciding with thedirection of zenith. As shown in the drawing, the drive section 125 isY-shaped as seen from the Y-axis direction in the drawing, and thesecond actuator can rotate the magnetic sensor unit 110 360 degrees onthe X-axis in the drawing.

The base portion 130 is a pedestal that supports other components, andis a pedestal on which the subject is placed during the heart magnetismmeasurement, in the present embodiment. The pole portion 140 supportsthe head 120 at the height of the chest of the subject. The pole portion140 may be capable of extending and contracting in an up-down directionto adjust the height of the magnetic sensor unit 110 to the height ofthe chest of the subject.

The information processing section 150 is a component for processing andoutputting measurement data obtained by the body portion 100, viadisplay, printing, or the like. The information processing section 150may be a computer such as a PC (personal computer), tablet computer,smartphone, work station, server computer, or general use computer, ormay be a computer system in which a plurality of computers areconnected. Instead, the information processing section 150 may be aspecialized computer designed for information processing of the heartmagnetism measurement, or may be specialized hardware realized byspecialized circuitry.

FIG. 2 shows a configuration of the magnetic sensor unit 110 accordingto the present embodiment. The magnetic sensor unit 110 includes amagnetic sensor array 210 and a sensor data collecting section 230. Themagnetic sensor array 210 is formed by a plurality of magnetic sensorcells 220 that are arranged three-dimensionally and are each capable ofdetecting a magnetic field in three axial directions, and each magneticsensor cell 220 includes a plurality of magnetoresistive elements. Inthe present drawing, the magnetic sensor array 210 includes fourmagnetic sensor cells 220 in the X direction, four magnetic sensor cells220 in the Y direction, and two magnetic sensor cells 220 in the Zdirection.

The sensor data collecting section 230 is electrically connected to theplurality of magnetic sensor cells 220 included in the magnetic sensorarray 210, collects the sensor data (detection signals) from theplurality of magnetic sensor cells 220, and supplies the sensor data tothe information processing section 150.

FIG. 3 shows a configuration and arrangement of the magnetic sensorcells 220 in the magnetic sensor array 210 according to the presentembodiment. Each magnetic sensor cell 220 includes a plurality of sensorsections 300 x to 300 z (collectively referred to below as the “sensorsections 300”) that each have a magnetoresistive element. In the presentembodiment, the sensor section 300 x is arranged in the X-axis directionand is capable of detecting a magnetic field in the X-axis direction.The sensor section 300 y is arranged in the Y-axis direction and iscapable of detecting a magnetic field in the Y-axis direction. Thesensor section 300 z is arranged in the Z-axis direction and is capableof detecting a magnetic field in the Z-axis direction.

The plurality of magnetic sensor cells 220 are arranged at regularintervals of Δx in the X-axis direction, Δy in the Y-axis direction, andΔz in the Z-axis direction. The position of each magnetic sensor cell220 in the magnetic sensor array 210 is expressed by j, which is a setof a position i in the X direction, a position j in the Y direction, anda position k in the Z direction. Here, i is an integer that satisfies0≤i≤Nx−1 (where Nx is the number of magnetic sensor cells 220 arrangedin the X direction), j is an integer that satisfies 0≤j≤Ny−1 (where Nyis the number of magnetic sensor cells 220 arranged in the Y direction),and k is an integer that satisfies 0≤k≤Nz−1 (where Nz is the number ofmagnetic sensor cells 220 arranged in the Z direction).

In the present drawing, the three axial directions of the magneticfields detected by the sensor sections 300 x, 300 y, and 300 z are thesame as the three-dimensional directions in which the magnetic sensorcells 220 are arranged. Therefore, it is easy to understand eachcomponent of the gradient magnetic field in the distribution diagram ofthe gradient magnetic field shown further below. Furthermore, the sensorsections 300 x, 300 y, and 300 z are arranged in each magnetic sensorcell 220 in a manner to not overlap with each other when viewed fromeach of the three dimensional directions in which the magnetic sensorcells 220 are arranged. Furthermore, in the present drawing, the sensorsections 300 x, 300 y, and 300 z are each arranged to have one endprovided on a side of a gap provided between the plurality of sensorsections 300 and to have another end that extends away from the gap inthe respective axial direction among the three axial directions. Thepresent drawing shows an example in which gaps are provided at the lowerleft corners of the magnetic sensor cells 220 as seen in a front view,and the sensor sections 300 x, 300 y, and 300 z are each arranged tohave one end provided in contact with the gap and the other endextending away from the gap in the respective axial direction among theX-axis, Y-axis, and Z-axis directions. In the present drawing, thesensor sections 300 x, 300 y, and 300 z are arranged along three edgesthat are perpendicular to each other from one corner in each cube shapedmagnetic sensor cell 220, and the gap is provided in this corner.Furthermore, the coils and magnets of the sensor sections 300 x, 300 y,and 300 z described further below are preferably arranged to not overlapwith each other. In this way, the measurement points can be made clear,and it becomes even easier to understand each component of the gradientmagnetic field. Furthermore, the cross-axes sensitivities of the sensorsections 300 x, 300 y, and 300 z can be treated as being equivalent toeach other. The cross-axis sensitivities are caused by interferencebetween the coils or magnets of the sensor sections 300 x, 300 y, and300 z. However, the three axial directions of magnetic fields that aredetected and the three dimensional directions in which the magneticsensor cells 220 are arranged may be different. If these directions aredifferent, there are no restrictions on the arrangement of the sensorsections 300 within the magnetic sensor cells 220 and the arrangementdirections of the magnetic sensor cells 220, and the degree of designfreedom for the magnetic sensor array 210 can be increased.

FIG. 4 shows an example of input/output characteristics of a magneticsensor of a magnetoresistive element according to the presentembodiment. In the present drawing, the horizontal axis indicates themagnitude B of the input magnetic field that is input to the magneticsensor, and the vertical axis indicates the magnitude V_xMR0 of thedetection signal of the magnetic sensor. The magnetic sensor includes agiant magneto-resistance (GMR) element, a tunnel magneto-resistanceelement (TMR), or the like, for example, and detects the magnitude ofthe magnetic field in a predetermined axial direction.

This type of magnetic sensor has high magnetic sensitivity, which is theslope of the detection signal V_xMR0 relative to the input magneticfield B, and can detect very small magnetic fields of approximately 10pT. On the other hand, the magnetic sensor has its detection signalV_xMR0 saturated when the absolute value of the input magnetic field Bis approximately 1 for example, and has a narrow range in which thelinearity of the input/output characteristic is favorable. Therefore,when a closed loop for generating a feedback magnetic field is added tosuch a magnetic sensor, it is possible to improve the linearity of themagnetic sensor. The following describes such a magnetic sensor.

FIG. 5 shows an example of a configuration of a sensor section 300according to the present embodiment. A sensor section 300 is providedwithin each of the plurality of magnetic sensor cell 220, and eachsensor section 300 includes a magnetic sensor 520, a magnetic fieldgenerating section 530, and an output section 540. A portion of thesensor section 300, e.g. an amplification circuit 532 and the outputsection 540, may be provided on the sensor data collecting section 230side instead of the magnetic sensor cell 220 side.

The magnetic sensor 520 includes a magnetic resistance effect elementsuch as a GMR element or TMR element, in the same manner as the magneticsensor described in FIG. 4. The magnetic sensor 520 may be formed suchthat, in a case where the positive direction of the magneticallysensitive axis is the +X direction, the resistance value increases whena magnetic field in the +X direction is input and the resistance valuedecreases when a magnetic field in the −X direction is input. In otherwords, by observing the change of the resistance value of the magneticsensor 520, it is possible to detect the magnitude of the magnetic fieldB input to this magnetic sensor 520. For example, with S representingthe magnetic sensitivity of the magnetic sensor 520, the result of thedetection of the input magnetic field B of the magnetic sensor 520 canbe calculated as S×B. As an example, the magnetic sensor 520 isconnected to a power source or the like, and outputs a voltage dropcorresponding to the change of the resistance value, as the inputmagnetic field detection result.

The magnetic field generating section 530 provides the magnetic sensor520 with a feedback magnetic field that reduces the input magnetic fielddetected by the magnetic sensor 520. For example, the magnetic fieldgenerating section 530 operates to generate a feedback magnetic fieldB_FB that has the opposite orientation of the magnetic field B input tothe magnetic sensor 520 and an absolute value that is substantially thesame as this input magnetic field, to cancel out the input magneticfield. The magnetic field generating section 530 includes anamplification circuit 532 and a coil 534.

The amplification circuit 532 outputs a current corresponding to thedetection result of the input magnetic field by the magnetic sensor 520,as a feedback current I_FB. For example, the amplification circuit 532includes a transconductance amplifier, and outputs the feedback currentI_FB corresponding to the output voltage of the magnetic sensor 520. Asan example, with G representing a voltage-current conversion coefficientof the amplification circuit 532, the feedback current I_FB can becalculated as G×S×B.

The coil 534 generates a feedback magnetic field B_FB corresponding tothe feedback current I_FB. The coil 534 preferably generates thefeedback magnetic field B_FB to be uniform across the entire magneticsensor 520. As an example, with β representing a coil coefficient of thecoil 534, the feedback magnetic field B_FB can be calculated as β×I_FB.Here, since the feedback magnetic field B_FB is generated with adirection for cancelling out the input magnetic field B, the magneticfield input to the magnetic sensor 520 is reduced to B-B_FB.Accordingly, the feedback current I_FB is expressed as shown in theexpression below.

I_FB=G×S×(B−β×I_FB)  Expression 1:

By solving Expression 1 for the feedback current I_FB, it is possible tocalculate the value of the feedback current I_FB in the regular state ofthe sensor sections 300. When the magnetic sensitivity S of the magneticsensor 520 and the voltage-current conversion coefficient G of theamplification circuit 532 are large enough, the expression shown belowcan be calculated from Expression 1.

$\begin{matrix}{{I\_ FB} = {\frac{G \times S \times B}{1 + {G \times S \times \beta}} \cong \frac{B}{\beta}}} & {{Expression}\mspace{14mu} 2}\end{matrix}$

The output section 540 outputs the output signal V_xMR corresponding tothe feedback current I_FB in order for the magnetic field generatingsection 530 to generate the feedback magnetic field B_FB. For example,the output section 540 includes a resistance element with a resistancevalue R, and outputs the voltage drop caused by the feedback currentI_FB flowing through this resistance element, as the output signalV_xMR. In this case, the output signal V_xMR is calculated as shown inthe expression below, according to Expression 2.

$\begin{matrix}{{V\_ xMR} = {{R \times {I\_ FB}} = \frac{R \times B}{\beta}}} & {{Expression}\mspace{14mu} 3}\end{matrix}$

As shown above, each sensor section 300 generates a feedback magneticfield that reduces the magnetic field input from the outside, andtherefore substantially reduces the magnetic field input to the magneticsensor 520. Therefore, the sensor section 300 uses a magnetoresistiveelement having the characteristic shown in FIG. 4 as the magnetic sensor520, and can prevent the detection signal V_xMR from becoming saturatedeven when the absolute value of the input magnetic field B exceeds 1 μT.The following describes the input/output characteristic of such a sensorsection 300.

FIG. 6 shows an example of an input/output characteristic of a sensorsection 300 according to the present embodiment. In the present drawing,the horizontal axis indicates the magnitude B of the input magneticfield that is input to the sensor section 300, and the vertical axisindicates the magnitude V_xMR of the detection signal of the sensorsection 300. The sensor section 300 has high magnetic sensitivity, andcan detect a very small magnetic field of approximately 10 pT.Furthermore, the sensor section 300 can maintain favorable linearity forthe detection signal V_xMR, even when the absolute value of the inputmagnetic field B exceeds 100 μT, for example.

In other words, the sensor section 300 according to the presentembodiment is configured such that the detection result maintainslinearity with respect to the input magnetic field B, when the inputmagnetic field B is in a predetermined range where the absolute value ofthe input magnetic field B is less than or equal to hundreds ofmicroteslas, for example. By using such a sensor section 300, it ispossible to easily detect a very weak magnetic signal, such as the heartmagnetism signal, for example.

FIG. 7 shows an example of a configuration of a magnetic sensor 520according to the present embodiment. As an example, the magnetic sensor520 according to the present embodiment includes a magnetoresistiveelement 702 and magnetic flux concentrators 704 and 706 arrangedrespectively at one end and the other end of the magnetoresistiveelement 702. The magnetic flux concentrators 704 and 706 are arranged ina manner to sandwich the magnetoresistive element 702 therebetween. Inthe front view of FIG. 7, the magnetic flux concentrator 704 arranged atthe right end of the magnetoresistive element 702 along the magneticallysensitive axis is the magnetic flux concentrator provided on thepositive side of the magnetically sensitive axis, and the magnetic fluxconcentrator 706 arranged on the left at the left end of themagnetoresistive element 702 is the magnetic flux concentrator providedon the negative side of the magnetically sensitive axis. The resistanceof the magnetoresistive element 702 may increase or decrease when amagnetic field oriented from the negative side to the positive side ofthe magnetically sensitive axis is input to the magnetic fluxconcentrators 704 and 706. The magnetically sensitive axis may bearranged along the direction of magnetization that is fixed by the fixedmagnetization layer forming the magnetoresistive element 702. Themagnetic flux concentrators 704 and 706 are formed by a soft magneticmaterial such as iron. By arranging the magnetic flux concentrators 704and 706 formed by the soft magnetic material respectively at the one endand the other end of the magnetoresistive element 702, it is possible toincrease the magnetic force lines passing through the magnetoresistiveelement 702, thereby making it possible to increase the sensitivity ofthe magnetic sensor 520.

In the present drawing, an example is shown in which the magnetic fluxconcentrators are provided respectively at the one end and the other endof the magnetoresistive element 702, but instead, a magnetic fluxconcentrator may be provided at only the one end or only the other endof the magnetoresistive element 702. However, in order to furtherincrease the sensitivity of the magnetic sensor 520, magnetic fluxconcentrators are preferably provided at both the one end and the otherend of the magnetoresistive element 702.

FIG. 8 shows a configuration of the magnetic sensor array 210, thesensor data collecting section 230, and a sensor data processing section800 according to the present embodiment.

The magnetic sensor array 210 includes a plurality of magnetic sensorcells 220. The plurality of magnetic sensor cells 220 each include theplurality of sensor sections 300 x to 300 z, as described above. Thepresent drawing shows, among the plurality of magnetic sensor cells 220oriented in the respective dimensional directions included in themagnetic sensor array 210, a portion relating to the calculation of afirst order gradient magnetic field at [i, j, k], i.e. a portionrelating to [i, j, k], [i+1, j, k], [i, j+1, k], and [i, j, k+1].

The sensor data collecting section 230 includes a plurality of ADconverters 810. The plurality of AD converters 810 are provided tocorrespond respectively to the plurality of sensor sections 300 x to 300z of the magnetic sensor cells 220, and each AD converter 810 convertsthe analog detection signal (the sensor output signal V_xMR of FIG. 6)output by the corresponding sensor section 300 into digital measurementdata (Vx, Vy, or Vz). Here, Vx, Vy and Vz are measurement values (e.g.digital values representing sensor output signal voltages) obtained bydigitally converting the detection signals from the sensor sections 300x, 300 y, and 300 z.

The sensor data processing section 800 includes a plurality of magneticfield acquiring sections 820, a plurality of calibration computingsections 830, and a plurality of data output sections 840 correspondingrespectively to the plurality of magnetic sensor cells 220, and alsoincludes a gradient magnetic field computing section 850.

Each magnetic field acquiring section 820 is connected to three ADconverters 810 that are connected to the corresponding magnetic sensorcell 220, and acquires the measurement data measured by each of thesensor sections 300 x to 300 z in this magnetic sensor cell 220, amongthe magnetic sensor cells 220 forming the magnetic sensor array 210.Specifically, the magnetic field acquiring section 820 may be formedusing a flip-flop or the like that latches at a prescribed timing T toacquire the digital measurement data (Vx, Vy, and Vz) that was digitallyconverted by the AD converter 810.

Each calibration computing section 830 is connected to the correspondingmagnetic field acquiring section 820, and calibrates the measurementdata acquired by the magnetic field acquiring section 820, using acalibration parameter. The basics of the measurement data calibrationperformed by the calibration computing section 830 are as describedbelow. Here, B (Bx, By, and Bz) represents the magnetic field input tothe magnetic sensor cell 220 at a position [i, j, k], and V (Vx, Vy, andVz) represents the detection results of the three-axis magnetic sensorobtained by the sensor sections 300 x, 300 y, and 300 z. In this case,with a matrix S representing the magnetic sensor characteristics of thethree-axis magnetic sensor, the detection result V of the three-axismagnetic sensor can be calculated as shown in the expression below.

$\begin{matrix}{\begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix} = {{{S\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix}} + \begin{pmatrix}{{Vos},x} \\{{Vos},y} \\{{Vos},z}\end{pmatrix}} = {{\begin{pmatrix}{Sxx} & {Sxy} & {Sxz} \\{Syx} & {Syy} & {Syz} \\{Szx} & {Szy} & {Szz}\end{pmatrix}\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix}} + \begin{pmatrix}{{Vos},x} \\{{Vos},y} \\{{Vos},z}\end{pmatrix}}}} & {{Expression}\mspace{14mu} 4}\end{matrix}$

Here, Sxx, Syy, and Szz respectively represent the sensitivities(main-axis sensitivities) in the main-axis directions of the sensorsections 300 x, 300 y, and 300 z, and Sxy, Sxz, Syx, Syz, Szx, and Szyrespectively represent the sensitivities (cross-axis sensitivities) inthe other-axis directions (also called cross-axis directions).Furthermore, (Vos, x), (Vos, y), and (Vos, z) respectively represent theoffsets of the sensor sections 300 x, 300 y, and 300 z. Here, themain-axis direction is the direction in which the sensor sections 300 x,300 y, and 300 z mainly perform measurement, and the cross-axisdirection is a direction that is mostly not measured. In the measurementby the magnetic sensor, the main-axis direction is a direction(input-axis direction or sensitivity-axis direction) in which themagnetic sensor exhibits maximum sensitivity when the magnetic field isinput thereto. And, the cross-axis direction is perpendicular to themain-axis direction. For example, when the sensor section 300 x performsmeasurement in the X-axis direction, the main-axis direction is alongthe X-axis, and the cross-axis directions are the Y-axis direction andthe Z-axis direction. The magnetic sensor 520 ideally has only themain-axis sensitivity, but sometimes has the cross-axis sensitivitiesdue to processing or the like. And, these cross-axis sensitivities causenon-orthogonal errors in measurements. Furthermore, the magnetic sensors520 also have the cross-axis sensitivities caused by interferencetherebetween.

Each sensor section 300 realizes linearity for the detection result withrespect to the input magnetic field, within the range of the inputmagnetic field to be detected, and therefore each element in the matrixS is a substantially constant coefficient that is unrelated to themagnitude of the input magnetic field B. Furthermore, even though eachsensor section 300 has cross-axis sensitivities, as long as thedetection result of the sensor section 300 has linearity, each elementof the matrix S is a substantially constant coefficient that isunrelated to the magnitude of the input magnetic field B.

Accordingly, by using the offsets ((Vos, x), (Vos, y), and (Vos, z)) andthe inverse matrix S⁻ of the matrix S, the calibration computing section830 can convert the measurement data (Vx, Vy, and Vz) into the magneticfield measurement data B (Bx, By, and Bz) indicating the originallyinput magnetic field. In other words, the calibration computing section830 calibrates the digital measurement data from the magnetic fieldacquiring section 820, using the main-axis sensitivities, the cross-axissensitivities, and the offsets. In this way, the calibration computingsection 830 corrects the offsets, the sensitivities in the main-axisdirections, and the sensitivities in the cross-axis directions. Thisconversion also occurs when the sensor sections 300 x to 300 z includethe magnetic flux concentrators described above. This is because themagnetic sensor cells 220 are formed as three-axis magnetic sensorsusing the sensor sections 300 x to 300 z, and because it enables theconversion using linear algebra. The offset calibration may be omittedin a case where the measurement data V is an AC component, by includinga high-pass filter or the like between the output of the sensor section300 and the calibration computing section 830. In other words, thecalibration computing section 830 may calibrate the digital measurementdata V from the magnetic field acquiring section 820 using at least oneof the main-axis sensitivities, the cross-axis sensitivities, and theoffsets.

$\begin{matrix}{\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix} = {S^{- 1}\{ {\begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix} - \begin{pmatrix}{{Vos},x} \\{{Vos},y} \\{{Vos},z}\end{pmatrix}} \}}} & {{Expression}\mspace{14mu} 5}\end{matrix}$

The calibration computing section 830 calculates the offsets ((Vos, x),(Vos, y), and (Vos, z)) and the inverse matrix S⁻¹ of the matrix S byusing environmental magnetic field measurement data, converts themeasurement data acquired by the magnetic field acquiring section 820into the magnetic field measurement data B using these calibrationparameters, and supplies the magnetic field measurement data B to thedata output section 840.

Since each sensor section 300 realizes linearity as described above, thecalibration computing section 830 can convert the measurement data intothe magnetic field measurement data B using substantially constantcoefficients. In other words, the substantially constant coefficientsused by the calibration computing section 830 can be determined as a setof calibration parameters using the environmental magnetic field data.

Furthermore, there are cases where certain magnetic sensor cells 220have different orientations than other magnetic sensor cells 220 withinthe same magnetic sensor array 210. Therefore, the calibration computingsection 830 may further perform a computation to align the orientationsof each of the magnetic sensor cells 220. In other words, thecalibration computing section 830 may perform a computation to align theorientations among a plurality of magnetic sensor cells 220. As anexample, with R representing an orientation conversion matrix forconverting the orientations of magnetic sensor cells into the sameorientation of the same coordinate system, the calibration computingsection 830 may perform the orientation alignment using a computationsuch as described below.

$\begin{matrix}{\begin{pmatrix}{Bx}^{\prime} \\{By}^{\prime} \\{Bz}^{\prime}\end{pmatrix} = {{R \cdot S^{- 1}}\{ {\begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix} - \begin{pmatrix}{{Vos},x} \\{{Vos},y} \\{{Vos},z}\end{pmatrix}} \}}} & {{Expression}\mspace{14mu} 6}\end{matrix}$

In this way, the outputs of all of the magnetic sensor cells are treatedas outputs of the same orientation in the same coordinate system, andtherefore, when there is a uniform environmental magnetic field, theoutputs of all of the magnetic sensor cells are the same, such that itis possible to cancel out the effect of a uniform environmental magneticfield in the computation of the gradient magnetic field describedfurther below. The orientation of each magnetic sensor cell may bealigned with the orientation of a magnetic sensor cell serving as areference. Alternatively, the orientation of each magnetic sensor cellmay be aligned with the orientation of a case of the magnetic sensorarray 210. An acceleration sensor may be further included in eachmagnetic sensor cell, and the orientation conversion matrix R may becalculated from the outputs of the acceleration sensors. Alternatively,the orientation conversion matrix may be calculated using the orthogonalconversion relationship between the outputs of the magnetic sensorcells. In other words, Da represents the measurement data matrix afterthe correction of Expression 5 has been performed for the output of acertain reference magnetic sensor cell 220, and Db represents themeasurement data matrix after the correction of Expression 5 has beenperformed on the output of another magnetic sensor cell 220 that is acorrection target when the same magnetic field is detected. At thistime, there is an orthogonal conversion relationship between Da and Db,and this can be calculated in the following manner. The matrix DaDb^(T),which is the product of the matrix Da and the transposed matrix of thematrix Db, is calculated, and singular-value decomposition is performedon this matrix DaDb^(T) to calculate the two unitary matrices U and W.At this time, R can be calculated by the equation R=UW^(T). Furthermore,the orientation conversion matrix R may be obtained by performing acalibration using a magnetic field that is already known. In this way,the calibration computing section 830 may correct the offsets of themeasurement data, the sensitivities in the main-axis directions, thesensitivities in the cross-axis directions, and the orientations.

The data output section 840 supplies the gradient magnetic fieldcomputing section 850 with the magnetic field measurement data B thathas been calibrated by the calibration computing section 830.

The gradient magnetic field computing section 850 calculates thegradient magnetic field using the magnetic field measurement data Bsupplied from the data output section 840, i.e. the magnetic fieldmeasurement data B in which the digital measurement data V has beencalibrated. In the present embodiment, the gradient magnetic fieldcomputing section 850 calculates the gradient magnetic field in allthree dimensions for the magnetic fields in all three axial directions.In this way, it is possible to obtain a more detailed gradient magneticfield distribution. Instead, the gradient magnetic field computingsection 850 may calculate the gradient magnetic field for only themagnetic fields in some of the three axial directions. Furthermore, thegradient magnetic field computing section 850 may calculate the gradientmagnetic field for only some of the directions among the threedimensional directions. In this way, it is possible to calculate onlythe necessary gradient magnetic field components, thereby reducing theload of the computation process performed by the gradient magnetic fieldcomputing section 850.

In the present embodiment, the three axial directions of the magneticfields being detected are the same as the three dimensional directionsin which the magnetic sensor cells 220 are arranged. Therefore, it iseasy to understand each component of the gradient magnetic field in thediagram of the gradient magnetic field distribution shown further below.Instead, the three axial directions of the magnetic fields beingdetected may be different than the three dimensional directions in whichthe magnetic sensor cells 220 are arranged. If these directions aredifferent, there are no restrictions on the arrangement of the sensorsections 300 within the magnetic sensor cells 220 and the arrangementdirections of the magnetic sensor cells 220, and the degree of designfreedom for the magnetic sensor array 210 can be increased.

The gradient magnetic field computing section 850 calculates thethree-dimensional gradient magnetic field for the magnetic fields in allthree axial directions, by calculating the difference between themagnetic fields of adjacent magnetic sensor cells 220 using the magneticfield measurement data measured between adjacent magnetic sensor cells220 among the plurality of magnetic sensor cells 220, i.e. bycalculating the difference between the pieces of magnetic fieldmeasurement data. The gradient magnetic field computing section 850 maycalculate a gradient magnetic field of the second-order or higher usingthe magnetic field measurement data measured between a plurality ofadjacent magnetic sensor cells 220.

FIG. 9 shows a flow for calculating an Nth-order gradient magneticfield. At step 910, the gradient magnetic field computing section 850substitutes 1 for n. At step 920, the gradient magnetic field computingsection 850 acquires the magnetic field measurement data measured by themagnetic sensor cells 220 at each of the positions. Here, the magneticfield measurement data measured by a magnetic sensor cell 220 at theposition [i, j, k] is expressed as shown by Expression 7 below.

B ^(i,j,k)=(B _(x) ^(i,j,k) ,B _(y) ^(i,j,k) ,B _(z)^(i,j,k))  Expression 7:

At step 930, the gradient magnetic field computing section 850calculates the first-order gradient magnetic field, by calculating thefirst-order difference between magnetic fields using the magnetic fieldmeasurement data between adjacent magnetic sensor cells 220 included inthe magnetic sensor array 210. The gradient magnetic field computingsection 850 calculates the first-order gradient magnetic field in theX-axis direction according to the expression shown below, using themagnetic field measurement data measured between the magnetic sensorcell 220 [i+1, j, k] and the magnetic sensor cell 220 [i, j, k].

$\begin{matrix}{\frac{B^{{i + 1},j,k} - B^{i,j,k}}{\Delta \; x} = ( {\frac{\Delta \; B_{x}^{i,j,k}}{\Delta \; x},\frac{\Delta \; B_{y}^{i,j,k}}{\Delta \; x},\frac{\Delta \; B_{z}^{i,j,k}}{\Delta \; x}} )^{T}} & {{Expression}\mspace{14mu} 8}\end{matrix}$

In other words, the gradient magnetic field computing section 850calculates the difference in the X-axis component of the magnetic fieldmeasurement data between the magnetic sensor cell 220 [i+1, j, k] andthe magnetic sensor cell 220 [i, j, k] by subtracting the X-axismagnetic field measurement data Bx^(i, j, k) of the magnetic sensor cell220 [i, j, k] from the X-axis magnetic field measurement dataBx^(i+1, j, k) of the magnetic sensor cell 220 [i+1, j, k], and dividesthe result of this subtraction by the distance Δx between the magneticsensor cell 220 [i+1, j, k] and the magnetic sensor cell 220 [i, j, k]to calculate the first-order gradient magnetic field in the X-axisdirection for the X-axis component of the magnetic field measurementdata at the position [i, j, k].

Similarly, the gradient magnetic field computing section 850 calculatesthe difference in the Y-axis component of the magnetic field measurementdata between the magnetic sensor cell 220 [i+1, j, k] and the magneticsensor cell 220 [i, j, k] by subtracting the Y-axis magnetic fieldmeasurement data By^(i, j, k) of the magnetic sensor cell 220 [i, j, k]from the Y-axis magnetic field measurement data By^(i+1, j, k) of themagnetic sensor cell 220 [i+1, j, k], and divides the result of thissubtraction by the distance Δx between the magnetic sensor cell 220[i+1, j, k] and the magnetic sensor cell 220 [i, j, k] to calculate thefirst-order gradient magnetic field in the X-axis direction for theY-axis component of the magnetic field measurement data at the position[i, j, k].

Similarly, the gradient magnetic field computing section 850 calculatesthe difference in the Z-axis component of the magnetic field measurementdata between the magnetic sensor cell 220 [i+1, j, k] and the magneticsensor cell 220 [i, j, k] by subtracting the Z-axis magnetic fieldmeasurement data Bz^(i, j, k) of the magnetic sensor cell 220 [i, j, k]from the Z-axis magnetic field measurement data Bz^(i+1, j, k) of themagnetic sensor cell 220 [i+1, j, k], and divides the result of thissubtraction by the distance Δx between the magnetic sensor cell 220[i+1, j, k] and the magnetic sensor cell 220 [i, j, k] to calculate thefirst-order gradient magnetic field in the X-axis direction for theZ-axis component of the magnetic field measurement data at the position[i, j, k].

Furthermore, the gradient magnetic field computing section 850calculates the first-order gradient magnetic field in the Y-axisdirection according to the following expression, using the magneticfield measurement data measured between the magnetic sensor cell 220 [i,j+1, k] and the magnetic sensor cell 220 [i, j, k], in the same manneras the calculation of the first-order gradient magnetic field in theX-axis direction.

$\begin{matrix}{\frac{B^{i,{j + 1},k} - B^{i,j,k}}{\Delta \; y} = ( {\frac{\Delta \; B_{x}^{i,j,k}}{\Delta \; y},\frac{\Delta \; B_{y}^{i,j,k}}{\Delta \; y},\frac{\Delta \; B_{z}^{i,j,k}}{\Delta \; y}} )^{T}} & {{Expression}\mspace{14mu} 9}\end{matrix}$

Yet further, the gradient magnetic field computing section 850calculates the first-order gradient magnetic field in the Z-axisdirection according to the following expression, using the magneticfield measurement data measured between the magnetic sensor cell 220 [i,j, k+1] and the magnetic sensor cell 220 [i, j, k], in the same manneras the calculation of the first-order gradient magnetic field in theX-axis direction.

$\begin{matrix}{\frac{B^{i,j,{k + 1}} - B^{i,j,k}}{\Delta \; z} = ( {\frac{\Delta \; B_{x}^{i,j,k}}{\Delta \; z},\frac{\Delta \; B_{y}^{i,j,k}}{\Delta \; z},\frac{\Delta \; B_{z}^{i,j,k}}{\Delta \; z}} )^{T}} & {{Expression}\mspace{14mu} 10}\end{matrix}$

According to the computations of Expressions 8 to 10, the gradientmagnetic field computing section 850 can obtain the first-order gradientmagnetic field shown below in Expression 11 in the three dimensionaldirections for the magnetic field measurement data on three axes. Inother words, the gradient magnetic field computing section 850 canobtain the gradient magnetic field in all of the three dimensionaldirections for the magnetic fields in all three axial directions. Thegradient magnetic field computing section 850 may calculate thefirst-order gradient magnetic field in units of the distance Δx=Δy=Δzbetween magnetic sensor cells 220. In this case, the gradient magneticfield computing section 850 can treat the difference between pieces ofmagnetic field measurement data as the first-order gradient magneticfield.

$\begin{matrix}\begin{bmatrix}\frac{\Delta \; B_{x}^{i,j,k}}{\Delta \; x} & \frac{\Delta \; B_{x}^{i,j,k}}{\Delta \; y} & \frac{\Delta \; B_{x}^{i,j,k}}{\Delta \; z} \\\frac{\Delta \; B_{y}^{i,j,k}}{\Delta \; x} & \frac{\Delta \; B_{y}^{i,j,k}}{\Delta \; y} & \frac{\Delta \; B_{y}^{i,j,k}}{\Delta \; z} \\\frac{\Delta \; B_{z}^{i,j,k}}{\Delta \; x} & \frac{\Delta \; B_{z}^{i,j,k}}{\Delta \; y} & \frac{\Delta \; B_{z}^{i,j,k}}{\Delta \; z}\end{bmatrix} & {{Expression}\mspace{14mu} 11}\end{matrix}$

At step 940, the gradient magnetic field computing section 850determines whether n is equal to N. If n is equal to N, the gradientmagnetic field computing section 850 ends the process. At step 940, if nis not equal to N, the gradient magnetic field computing section 850moves the process to step 950, and increments n by 1. The gradientmagnetic field computing section 850 then moves the process to step 960.

At step 960, the gradient magnetic field computing section 850calculates the nth-order gradient magnetic field using the (n−1)th-ordergradient magnetic field. As an example, at step 930 before thecalculation of the second-order gradient magnetic field, the gradientmagnetic field computing section 850 has already calculated thefirst-order gradient magnetic field at the position [i+1, j, k]according to the following expression, using Expression 8 and themagnetic field measurement data measured between the magnetic sensorcell 220 [i+2, j, k] and the magnetic sensor cell 220 [i+1, j, k] as thefirst-order gradient magnetic field in the X-axis direction.

$\begin{matrix}{\frac{B^{{i + 2},j,k} - B^{{i + 1},j,k}}{\Delta \; x} = ( {\frac{\Delta \; B_{x}^{{i + 1},j,k}}{\Delta \; x},\frac{\Delta \; B_{y}^{{i + 1},j,k}}{\Delta \; x},\frac{\Delta \; B_{z}^{{i + 1},j,k}}{\Delta \; x}} )^{T}} & {{Expression}\mspace{14mu} 12}\end{matrix}$

Then, at step 960, when calculating the second-order gradient magneticfield, the gradient magnetic field computing section 850 calculates thesecond-order gradient magnetic field in the X-axis direction accordingto the following expression, using the first-order gradient magneticfield calculated using Expression 8 and Expression 12.

$\begin{matrix}{\frac{\frac{B^{{i + 2},j,k} - B^{{i + 1},j,k}}{\Delta \; x} - \frac{B^{{i + 1},j,k} - B^{i,j,k}}{\Delta \; x}}{\Delta \; x} = ( {\frac{\Delta^{2}B_{x}^{i,j,k}}{\Delta \; x^{2}},\frac{\Delta^{2}B_{y}^{i,j,k}}{\Delta \; x^{2}},\frac{\Delta^{2}B_{z}^{i,j,k}}{\Delta \; x^{2}}} )^{T}} & {{Expression}\mspace{14mu} 13}\end{matrix}$

In other words, the gradient magnetic field computing section 850calculates the second-order gradient magnetic field in the X-axisdirection by subtracting the first-order gradient magnetic field in theX-axis direction at the position [i, j, k] from the first-order gradientmagnetic field in the X-axis direction at the position [i+1, j, k] anddividing the result of the subtraction by the distance ΔX between theadjacent magnetic sensor cells 220 in the X-axis direction.

The gradient magnetic field computing section 850 can calculate thesecond-order gradient magnetic fields in the Y-axis direction and theZ-axis direction in the same manner as the second-order gradientmagnetic field in the X-axis direction. Next, the gradient magneticfield computing section 850 returns the process to step 940, and repeatsthe subsequent processes. In this way, the gradient magnetic fieldcomputing section 850 can acquire the nth-order gradient magnetic fieldsin the three dimensional directions for the magnetic field measurementdata on three axes, using the magnetic field measurement data measuredbetween adjacent magnetic sensor cells 220.

Here, if N=1, the gradient magnetic field computing section 850 canexpress the first-order gradient magnetic field provided by Expression11 obtained from step 930, as shown in the expression below, if Δx=Δy=Δzis small enough

$\begin{matrix}\begin{bmatrix}\frac{\partial B_{x}^{i,j,k}}{\partial x} & \frac{\partial B_{x}^{i,j,k}}{\partial y} & \frac{\partial B_{x}^{i,j,k}}{\partial z} \\\frac{\partial B_{y}^{i,j,k}}{\partial x} & \frac{\partial B_{y}^{i,j,k}}{\partial y} & \frac{\partial B_{y}^{i,j,k}}{\partial z} \\\frac{\partial B_{z}^{i,j,k}}{\partial x} & \frac{\partial B_{z}^{i,j,k}}{\partial y} & \frac{\partial B_{z}^{i,j,k}}{\partial z}\end{bmatrix} & {{Expression}\mspace{14mu} 14}\end{matrix}$

If N=2, the gradient magnetic field computing section 850 acquires thesecond-order gradient magnetic field shown below, using the first-ordergradient magnetic field and the flow shown in the present drawing.

$\begin{matrix}\begin{bmatrix}\frac{\partial^{2}B_{x}^{i,j,k}}{\partial x^{2}} & \frac{\partial^{2}B_{x}^{i,j,k}}{\partial y^{2}} & \frac{\partial^{2}B_{x}^{i,j,k}}{\partial z^{2}} \\\frac{\partial^{2}B_{y}^{i,j,k}}{\partial x^{2}} & \frac{\partial^{2}B_{y}^{i,j,k}}{\partial y^{2}} & \frac{\partial^{2}B_{y}^{i,j,k}}{\partial z^{2}} \\\frac{\partial^{2}B_{z}^{i,j,k}}{\partial x^{2}} & \frac{\partial^{2}B_{z}^{i,j,k}}{\partial y^{2}} & \frac{\partial^{2}B_{z}^{i,j,k}}{\partial z^{2}}\end{bmatrix} & {{Expression}\mspace{14mu} 15}\end{matrix}$

If N is greater than 2, the gradient magnetic field computing section850 acquires the nth-order gradient magnetic field shown below, usingthe first-order and second-order gradient magnetic fields and the flowshown in the present drawing.

$\begin{matrix}\begin{bmatrix}\frac{\partial^{n}B_{x}^{i,j,k}}{\partial x^{n}} & \frac{\partial^{n}B_{x}^{i,j,k}}{\partial y^{n}} & \frac{\partial^{n}B_{x}^{i,j,k}}{\partial z^{n}} \\\frac{\partial^{n}B_{y}^{i,j,k}}{\partial x^{n}} & \frac{\partial^{n}B_{y}^{i,j,k}}{\partial y^{n}} & \frac{\partial^{n}B_{y}^{i,j,k}}{\partial z^{n}} \\\frac{\partial^{n}B_{z}^{i,j,k}}{\partial x^{n}} & \frac{\partial^{n}B_{z}^{i,j,k}}{\partial y^{n}} & \frac{\partial^{n}B_{z}^{i,j,k}}{\partial z^{n}}\end{bmatrix} & {{Expression}\mspace{14mu} 16}\end{matrix}$

Here, in a conventional Z-axis SQUID gradiometric array shown in PatentDocument 1, it is impossible to acquire the ∂Bx/∂x, ∂Bx/∂y, ∂Bx/∂z,∂By/∂x, ∂By/∂y, and ∂By/∂z components. Furthermore, with theconventional X-Y-axis SQUID gradiometric array shown in Patent Document1, it is impossible to acquire the ∂Bx/∂z, ∂By/∂z, ∂Bz/∂x, ∂Bz/∂y, and∂Bz/∂z components. In contrast to this, according to the magnetic fieldmeasurement apparatus 10 of the present embodiment, as shown inExpressions 14, 15, and 16, it is possible to obtain the gradientmagnetic fields in the three dimensional directions for the magneticfield measurement data on three axes, without missing any components.Furthermore, according to the magnetic field measurement apparatus 10 ofthe present embodiment, the computation is performed from the magneticfields between adjacent magnetic sensor cells 220, and therefore it ispossible to obtain not only the second-order and higher gradientmagnetic fields in only the X-axis direction, Y-axis direction, andZ-axis direction, but also to obtain the gradient magnetic fieldcomponents corresponding to a format that is partially differentiated indifferent axial directions, such as the ∂²B/∂x∂y, ∂²B/∂y∂z, and ∂²B/∂z∂xcomponents.

Furthermore, according to the magnetic field measurement apparatus 10 ofthe present embodiment, it is possible to acquire the gradient magneticfields in the three dimensional directions without missing anycomponents, and therefore, for the heart magnetism measurement, forexample, it is possible to simultaneously implement a measurement usingtangent components and a measurement using normal components. As anexample, as shown in FIG. 1, a vector arrow diagram is created using thegradient magnetic fields of the tangent components (∂Bx/∂z and ∂By/∂z),for example, in the XY plane parallel to the change of the person. Asanother example, a vector arrow diagram is created using the gradientmagnetic fields of the normal components (∂Bz/∂x and ∂Bz/∂y). Here, thevector arrow diagram is also referred to as a current arrow diagram, andis obtained according to the following expression when using therepresentative gradient magnetic fields of the normal components (∂Bx/∂zand ∂By/∂z).

$\begin{matrix}{I_{xy} = {{\frac{\partial B_{z}}{\partial y}e_{x}} - {\frac{\partial B_{z}}{\partial x}e_{y}}}} & {{Expression}\mspace{14mu} 17}\end{matrix}$

Here, ex and ey are unit vectors in the X direction and the Y direction.When using the tangent components, (∂Bz/∂z and ∂By/∂z) may be replacedwith (−∂Bz/∂x and −∂Bz/∂y). The above assumes that the magnetic fieldsource is projected onto the XY plane, but according to the magneticfield measurement apparatus 10 of the present embodiment, thisprojection can be expanded three-dimensionally. In other words, it ispossible to create a vector arrow diagram projected onto the YZ planeand the XZ plane. Accordingly, the gradient magnetic field computingsection 850 may further compute and output a two-dimensional vectorarrow diagram or a three-dimensional vector arrow diagram (vector arrowdiagram in the XY plane, the YZ plane, and the XZ plane). According tothe magnetic field measurement apparatus 10 of the present embodiment,each sensor section 300 of the magnetic sensor 520 realizes linearityand can widen the input range of the magnetic field, and therefore bysetting the magnetic field measurement data of each magnetic sensor cellas output (in the same orientation) in the same coordinate system usingthe calibration computing section 830, it is possible to calculate thegradient magnetic fields in which uniform magnetic fields are cancelledout in the computation performed by the gradient magnetic fieldcomputing section 850. Accordingly, the magnetic field measurementapparatus 10 of the present embodiment enables the usage of a gradientmagnetic field computation even in an environment where there isgeomagnetism and no shield room.

FIG. 10 shows an example of a first-order gradient magnetic fielddistribution obtained by the magnetic field measurement apparatus 10according to the present embodiment. FIG. 11 shows an example of asecond-order gradient magnetic field distribution obtained by themagnetic field measurement apparatus 10 according to the presentembodiment. These drawings show gradient magnetic field distributions inwhich a magnet with dimensions of X=5 mm, Y=0.5 mm, and Z=0.5 mm isarranged at the position (X, Y)=(0, −5 cm) with its N pole facing in thepositive X-axis direction, a magnet with dimensions of X=5 mm, Y=0.5 mm,and Z=0.5 mm is arranged at the position (X, Y)=(0, 5 cm) with its Npole facing in the negative X-axis direction, and a plane that is 30cm×30 cm, with grid points at 1 cm intervals, is measured by themagnetic field measurement apparatus 10 at a height of Z=1 cm from theplane in which the magnets are placed. In these drawings, the dotdensity at each coordinate indicates the gradient magnetic field inarbitrary units, and a lower dot density indicates a larger gradientmagnetic field. FIG. 10 shows the ∂Bx/∂x component in the first-ordergradient magnetic field distribution obtained under these conditions,and FIG. 11 shows the ∂²Bx/∂x² component in the second-order gradientmagnetic field distribution obtained under these conditions.

As shown in FIGS. 10 and 11, according to the magnetic field measurementapparatus 10 of the present embodiment, it is possible to obtain agradient magnetic field distribution in which the calculated gradientmagnetic field is visible. In the present drawings, only examples of the∂Bx/∂x component in the first-order gradient magnetic field distributionand the ∂²Bx/∂x² component in the second-order gradient magnetic fielddistribution are shown, but the magnetic field measurement apparatus 10can obtain similar gradient magnetic field distributions for othergradient components and for third-order or higher gradient magneticfields.

FIG. 12 shows a configuration of the magnetic sensor array 210, thesensor data collecting section 230, the sensor data processing section800, and a malfunction determining section 1200 according to amodification of the magnetic field measurement apparatus 10. In thepresent modification, the magnetic field measurement apparatus 10further includes the malfunction determining section 1200. Themalfunction determining section 1200 determines malfunctions of themagnetic sensor array 210, based on the gradient magnetic fieldscalculated by the gradient magnetic field computing section 850.

FIG. 13 shows a malfunction determination flow. At step 1310, themalfunction determining section 1200 calculates a value indicating therotation of a magnetic field at a position of any magnetic sensor cell220 among the plurality of magnetic sensor cells 220, based on thegradient magnetic field obtained from the process flow of FIG. 9, forexample.

At step 1320, the malfunction determining section 1200 determineswhether the calculated value indicating the rotation of the magneticfield is greater than or equal to a first threshold value. If thecalculated value indicating the rotation of the magnetic field isgreater than or equal to the first threshold value, the malfunctiondetermining section 1200 determines that the magnetic sensor array 210is malfunctioning.

The following describes this determination. If the determination isbased on a vector analysis, when the magnetic field measured by themagnetic sensor cell 220 at the position id is provided by Expression 7,the rotation is expressed by a vector function in which the respectivecomponents are the difference between ∂Bz^(i, j, k)/∂y and∂By^(i, j, k)/∂z, the difference between ∂Bx^(i, j, k)/∂z and∂Bz^(i, j, k)/∂X, and the difference between ∂By^(i, j, k)/∂X and∂Bx^(i, j, k)/∂y, as shown in the following expression.

$\begin{matrix}{{{rot}\mspace{14mu} B^{i,j,k}} = ( {{\frac{\partial B_{z}^{i,j,k}}{\partial y} - \frac{\partial B_{y}^{i,j,k}}{\partial z}},{\frac{\partial B_{x}^{i,j,k}}{\partial z} - \frac{\partial B_{z}^{i,j,k}}{\partial x}},{\frac{\partial B_{y}^{i,j,k}}{\partial x} - \frac{\partial B_{x}^{i,j,k}}{\partial y}}} )} & {{Expression}\mspace{14mu} 18}\end{matrix}$

Here, the generation of the magnetic field occurs due to the current andthe change over time of the electrical field based on a Maxwellequation. However, there is no current source in the magnetic sensorarray 210. Therefore, the rotation of the magnetic field at the positionid is 0, i.e. rot B=0. In other words, each component in the vectorfunction shown by Expression 18 becomes 0 in theory.

Accordingly, the malfunction determining section 1200 can obtain thedifference between ∂Bz^(i, j, k)/∂y and ∂By^(i, j, k)/∂z, the differencebetween ∂Bx^(i, j, k)/∂z and ∂Bz^(i, j, k)/∂x, and the differencebetween ∂By^(i, j, k)/∂x and ∂Bx^(i, j, k)/∂y from the differencesbetween the symmetric components of the gradient magnetic fields shownin Expression 14, for example, set the absolute values of thedifferences between these symmetric components to be the valuesindicating the rotation of the magnetic field at the position [i, j, k],and determine that the magnetic sensor array 210 is malfunctioning ifany of these values is significantly far from 0, i.e. if any of thesevalues is greater than or equal to the first threshold value.

In the above description, a case is described in which the magneticsensor array 210 is determined to be malfunctioning if any one of thecomponents in the vector function shown in Expression 18 issignificantly far from 0, but instead, the malfunction determiningsection 1200 may determine that the magnetic sensor array 210 ismalfunctioning if the magnitude of the vector function shown inExpression 18 is significantly far from 0. In this case, the malfunctiondetermining section 1200 sets the square root of the total sum of thesquare of the difference between ∂Bz^(i, j, k)/∂y and ∂By^(i, j, k)/∂z,the square of the difference between ∂Bx^(i, j, k)/∂Z and∂Bz^(i, j, k)/∂x, and the square of the difference between∂By^(i, j, k)/∂x and ∂Bx^(i, j, k)/∂y as a value indicating the rotationof the magnetic field at the position [i, j, k], and determines that themagnetic sensor array 210 is malfunctioning if this value issignificantly far from 0, i.e. if this value is greater than or equal tothe first threshold value.

At step 1320, if the value indicating the rotation of the magnetic fieldis less than the first threshold value, the malfunction determiningsection 1200 moves the process to step 1330. At step 1330, themalfunction determining section 1200 calculates a value indicating thedivergence of the magnetic field at the position of any magnetic sensorcell 220 among the plurality of magnetic sensor cells 220, based on thegradient magnetic field obtained from the process flow of FIG. 9, forexample.

At step 1340, the malfunction determining section 1200 determineswhether the calculated value indicating the divergence of the magneticfield is greater than or equal to a second threshold value. Themalfunction determining section 1200 determines that the magnetic sensorarray 210 is malfunctioning if the calculated value indicating thedivergence of the magnetic field is greater than or equal to the secondthreshold value.

The following describes this determination. If the determination isbased on a vector analysis, when the magnetic field measured by themagnetic sensor cell 220 at the position [i, j, k] is provided byExpression 7, the divergence is expressed by a scalar function that isthe sum of ∂Bx^(i, j, k)/∂X, ∂By^(i, j, k)/∂y, and ∂Bz^(i, j, k)/∂z.

$\begin{matrix}{{{div}\mspace{14mu} B^{i,j,k}} = {\frac{\partial B_{x}^{i,j,k}}{\partial x} + \frac{\partial B_{y}^{i,j,k}}{\partial y} + \frac{\partial B_{z}^{i,j,k}}{\partial z}}} & {{Expression}\mspace{14mu} 19}\end{matrix}$

Here, the magnetic force lines are certain to become closed curve linesbased on a Maxwell equation. Therefore, the divergence of the magneticfield at the position [i, j, k] is 0, i.e. div B=0. In other words,value of the scalar function shown by Expression 19 becomes 0 in theory.

Accordingly, the malfunction determining section 1200 can obtain the sumof ∂Bx^(i, j, k)/∂X, ∂By^(i, j, k)/∂y, and ∂Bz^(i, j, k)/∂z from thediagonal components shown in Expression 14, for example, set theabsolute value of the sum of these diagonal components to be the valueindicating the divergence of the magnetic field at the position j, anddetermine that the magnetic sensor array 210 is malfunctioning if thisvalue is significantly far from 0, i.e. if this value is greater than orequal to the second threshold value.

At step 1340, if the value indicating the divergence of the magneticfield is less than the second threshold value, the magnetic sensor array210 is determined to be operating correctly. In this way, by acquiringthe gradient magnetic field in the three dimensional directions for themagnetic field measurement data on three axes without missing anycomponents, it is possible to detect whether the magnetic sensor array210 is malfunctioning using this gradient magnetic field. Furthermore,it is possible to identify the position in the magnetic sensor array 210where the malfunction occurred, based on the position of the gradientmagnetic field used for performing the malfunction determination.

FIG. 14 shows a modification of the magnetic sensor array 210 accordingto the present embodiment. In FIG. 14, the components that have the samefunction and configuration as in FIG. 3 are given the same referencenumerals, and only differing points are included in the followingdescription. In the present drawing, each of the plurality of magneticsensor cells 220 in the magnetic sensor array 210 is provided with thesensor sections 300 x, 300 y, and 300 z without being provided with thegap in the corner thereof. In this way, even when the sensor sections300 are arranged in this manner, each magnetic sensor cell 220 can bearranged such that the sensor sections 300 x, 300 y, and 300 z do notoverlap when seen respectively from the three dimensional directionsalong the X-axis, Y-axis, and Z-axis. With such an arrangement, theplurality of sensor sections 300 x, 300 y, and 300 z can be arranged ina dispersed manner within the magnetic sensor cell 220, and it ispossible to prevent an arrangement in which the plurality of sensorsections 300 x, 300 y, and 300 z are gathered in one corner. Themagnetic field measurement apparatus 10 of the present embodiment mayacquire the measurement data using the magnetic sensor array 210 inwhich the sensor sections 300 are arranged in this manner.

Various embodiments of the present invention may be described withreference to flowcharts and block diagrams whose blocks may represent(1) steps of processes in which operations are performed or (2) sectionsof apparatuses responsible for performing operations. Certain steps andsections may be implemented by dedicated circuitry, programmablecircuitry supplied with computer-readable instructions stored oncomputer-readable media, and/or processors supplied withcomputer-readable instructions stored on computer-readable media.Dedicated circuitry may include digital and/or analog hardware circuitsand may include integrated circuits (IC) and/or discrete circuits.Programmable circuitry may include reconfigurable hardware circuitscomprising logical AND, OR, XOR, NAND, NOR, and other logicaloperations, flip-flops, registers, memory elements, etc., such asfield-programmable gate arrays (FPGA), programmable logic arrays (PLA),and the like.

The computer-readable medium may be a tangible device that can storeinstructions to be executed by a suitable device, and as a result, acomputer-readable medium having instructions stored thereon is a productthat includes instructions that can be executed in order to create themeans for executing the operations designated by flow charts and blockdiagrams. Examples of the computer-readable medium may include anelectronic storage device, a magnetic storage device, an optical storagedevice, an electromagnetic storage medium, a magnetic storage medium, anoptical storage medium, an electromagnetic storage medium, asemiconductor storage medium, and the like. Specific examples of thecomputer-readable medium may include a floppy (Registered Trademark)disk, a diskette, a hard disk, a random access memory (RAM), a read-onlymemory (ROM), an erasable programmable read-only memory (EPROM or Flashmemory), an electrically erasable programmable read-only memory(EEPROM), a static random access memory (SRAM), a portable compact discread-only memory (CD-ROM), a digital versatile disk (DVD), a Blu-ray(Registered Trademark) disk, a memory stick, an integrated circuit card,or the like.

The computer-readable instructions may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, JAVA (RegisteredTrademark), C++ or the like, and conventional procedural programminglanguages, such as the “C” programming language or similar programminglanguages.

The computer-readable instructions may be provided to a processor orprogrammable circuitry of a general purpose computer, special purposecomputer, or other programmable data processing apparatus to produce amachine, either locally, via a local area network (LAN), or via a widearea network (WAN) such as the Internet, and may be executed to createthe means for performing the operations designated by the flow chartsand block diagrams. Examples of the processor include a computerprocessor, a processing unit, a microprocessor, a digital signalprocessor, a controller, a microcontroller, and the like.

FIG. 15 shows an example of a computer 2200 in which aspects of thepresent invention may be wholly or partly embodied. A program that isinstalled in the computer 2200 can cause the computer 2200 to functionas or perform operations associated with apparatuses of the embodimentsof the present invention or one or more sections thereof, and/or causethe computer 2200 to perform processes of the embodiments of the presentinvention or steps thereof. Such a program may be executed by the CPU2212 to cause the computer 2200 to perform certain operations associatedwith some or all of the blocks of flowcharts and block diagramsdescribed herein.

The computer 2200 according to the present embodiment includes a CPU2212, a RAM 2214, a graphic controller 2216, and a display device 2218,which are mutually connected by a host controller 2210. The computer2200 also includes input/output units such as a communication interface2222, a hard disk drive 2224, a DVD-ROM drive 2226 and an IC card drive,which are connected to the host controller 2210 via an input/outputcontroller 2220. The computer also includes legacy input/output unitssuch as a ROM 2230 and a keyboard 2242, which are connected to theinput/output controller 2220 through an input/output chip 2240.

The CPU 2212 operates according to programs stored in the ROM 2230 andthe RAM 2214, thereby controlling each unit. The graphic controller 2216obtains image data generated by the CPU 2212 on a frame buffer or thelike provided in the RAM 2214 or in itself, and causes the image data tobe displayed on the display device 2218.

The communication interface 2222 communicates with other electronicdevices via a network. The hard disk drive 2224 stores programs and dataused by the CPU 2212 within the computer 2200. The DVD-ROM drive 2226reads the programs or the data from the DVD-ROM 2201, and provides thehard disk drive 2224 with the programs or the data via the RAM 2214. TheIC card drive reads programs and data from an IC card, and/or writesprograms and data into the IC card.

The ROM 2230 stores therein a boot program or the like executed by thecomputer 2200 at the time of activation, and/or a program depending onthe hardware of the computer 2200. The input/output chip 2240 may alsoconnect various input/output units via a parallel port, a serial port, akeyboard port, a mouse port, and the like to the input/output controller2220.

A program is provided by computer readable media such as the DVD-ROM2201 or the IC card. The program is read from the computer readablemedia, installed into the hard disk drive 2224, RAM 2214, or ROM 2230,which are also examples of computer readable media, and executed by theCPU 2212. The information processing described in these programs is readinto the computer 2200, resulting in cooperation between a program andthe above-mentioned various types of hardware resources. An apparatus ormethod may be constituted by realizing the operation or processing ofinformation in accordance with the usage of the computer 2200.

For example, when communication is performed between the computer 2200and an external device, the CPU 2212 may execute a communication programloaded onto the RAM 2214 to instruct communication processing to thecommunication interface 2222, based on the processing described in thecommunication program. The communication interface 2222, under controlof the CPU 2212, reads transmission data stored on a transmissionbuffering region provided in a recording medium such as the RAM 2214,the hard disk drive 2224, the DVD-ROM 2201, or the IC card, andtransmits the read transmission data to a network or writes receptiondata received from a network to a reception buffering region or the likeprovided on the recording medium.

In addition, the CPU 2212 may cause all or a necessary portion of a fileor a database to be read into the RAM 2214, the file or the databasehaving been stored in an external recording medium such as the hard diskdrive 2224, the DVD-ROM drive 2226 (DVD-ROM 2201), the IC card, etc.,and perform various types of processing on the data on the RAM 2214. TheCPU 2212 may then write back the processed data to the externalrecording medium.

Various types of information, such as various types of programs, data,tables, and databases, may be stored in the recording medium to undergoinformation processing. The CPU 2212 may perform various types ofprocessing on the data read from the RAM 2214, which includes varioustypes of operations, processing of information, condition judging,conditional branch, unconditional branch, search/replace of information,etc., as described throughout this disclosure and designated by aninstruction sequence of programs, and writes the result back to the RAM2214. In addition, the CPU 2212 may search for information in a file, adatabase, etc., in the recording medium. For example, when a pluralityof entries, each having an attribute value of a first attributeassociated with an attribute value of a second attribute, are stored inthe recording medium, the CPU 2212 may search for an entry matching thecondition whose attribute value of the first attribute is designated,from among the plurality of entries, and read the attribute value of thesecond attribute stored in the entry, thereby obtaining the attributevalue of the second attribute associated with the first attributesatisfying the predetermined condition.

The above-explained program or software modules may be stored in thecomputer readable media on or near the computer 2200. In addition, arecording medium such as a hard disk or a RAM provided in a serversystem connected to a dedicated communication network or the Internetcan be used as the computer readable media, thereby providing theprogram to the computer 2200 via the network.

While the embodiments of the present invention have been described, thetechnical scope of the invention is not limited to the above describedembodiments. It will be apparent to persons skilled in the art thatvarious alterations and improvements can be added to the above-describedembodiments. It should also apparent from the scope of the claims thatthe embodiments added with such alterations or improvements are withinthe technical scope of the invention.

The operations, procedures, steps, and stages of each process performedby an apparatus, system, program, and method shown in the claims,embodiments, or diagrams can be performed in any order as long as theorder is not indicated by “prior to,” “before,” or the like and as longas the output from a previous process is not used in a later process.Even if the process flow is described using phrases such as “first” or“next” in the claims, embodiments, or diagrams, it does not necessarilymean that the process must be performed in this order.

What is claimed is:
 1. A magnetic field measurement apparatuscomprising: a magnetic sensor array having a plurality of magneticsensor cells capable of detecting magnetic fields in three axialdirections arranged in three dimensions, each magnetic sensor cellincluding a plurality of magnetic sensors that each have amagnetoresistive element and a magnetic flux concentrator arranged atleast at one of one end and another end of the magnetoresistive element;a plurality of AD converters that respectively convert analog detectionsignals output by the plurality of magnetic sensors into digitalmeasurement data; a magnetic field acquiring section that acquires thedigital measurement data; a calibration computing section thatcalibrates the digital measurement data from the magnetic fieldacquiring section, using at least one of a main-axis sensitivity,cross-axis sensitivities, and an offset; and a gradient magnetic fieldcomputing section that calculates a gradient magnetic field usingmagnetic field measurement data resulting from the calibration of thedigital measurement data, wherein the gradient magnetic field computingsection calculates the gradient magnetic field in three dimensions formagnetic fields in all three axial directions, by calculating adifference in magnetic fields between adjacent magnetic sensor cellsamong the plurality of magnetic sensor cells, using the magnetic fieldmeasurement data measured between the adjacent magnetic sensor cells. 2.The magnetic field measurement apparatus according to claim 1, whereinthe three axial directions and directions in which of the threedimensions the magnetic sensor cells are arranged are the same.
 3. Themagnetic field measurement apparatus according to claim 1, wherein thegradient magnetic field computing section calculates the gradientmagnetic field that is second-order or higher, using the measurementdata measured between a plurality of pairs of the adjacent magneticsensor cells.
 4. The magnetic field measurement apparatus according toclaim 1, wherein the plurality of magnetic sensor cells each include aplurality of sensor sections that each include the magnetic sensor and acoil, and the plurality of sensor sections are arranged in a manner tonot overlap with each other when viewed from each of the threedimensional directions.
 5. The magnetic field measurement apparatusaccording to claim 4, wherein the plurality of sensor sections are eacharranged such that one end is provided at a gap located between theplurality of sensor sections and another end extends away from the gapin a corresponding axial direction among the three axial directions. 6.The magnetic field measurement apparatus according to claim 1, furthercomprising: a malfunction determining section that determines amalfunction of the magnetic sensor array, based on the gradient magneticfield calculated by the gradient magnetic field computing section. 7.The magnetic field measurement apparatus according to claim 6, whereinthe malfunction determining section calculates a value indicatingrotation of the magnetic field at a position of any magnetic sensor cellamong the plurality of magnetic sensor cells, based on the gradientmagnetic field, and determines that the magnetic sensor array ismalfunctioning if the value indicating the rotation of the magneticfield is greater than or equal to a first threshold value.
 8. Themagnetic field measurement apparatus according to claim 6, wherein themalfunction determining section calculates a value indicating divergenceof the magnetic field at a position of any magnetic sensor cell amongthe plurality of magnetic sensor cells, based on the gradient magneticfield, and determines that the magnetic sensor array is malfunctioningif the value indicating the divergence of the magnetic field is greaterthan or equal to a second threshold value.
 9. The magnetic fieldmeasurement apparatus according to claim 1, wherein the calibrationcomputing section performs a computation to align orientations of theplurality of magnetic sensor cells.
 10. A magnetic field measurementmethod for measuring a magnetic field with a magnetic field measurementapparatus, the magnetic field measurement method comprising: converting,with the magnetic field measurement apparatus, analog detection signalsoutput respectively by a plurality of magnetic sensors, in a magneticsensor array having a plurality of magnetic sensor cells capable ofdetecting magnetic fields in three axial directions arranged in threedimensions, with each magnetic sensor cell including a plurality of themagnetic sensors that each have a magnetoresistive element and amagnetic flux concentrator arranged at least at one of one end andanother end of the magnetoresistive element, into digital measurementdata; acquiring the digital measurement data; calibrating the digitalmeasurement data using at least one of a main-axis sensitivity,cross-axis sensitivities, and an offset; and calculating a gradientmagnetic field using magnetic field measurement data resulting from thecalibration of the digital measurement data, wherein the calculating thegradient magnetic field includes calculating the gradient magnetic fieldin three dimensions for magnetic fields in all three axial directions,by calculating a difference in magnetic fields between adjacent magneticsensor cells among the plurality of magnetic sensor cells, using themagnetic field measurement data measured between the adjacent magneticsensor cells.
 11. A storage medium storing thereon a magnetic fieldmeasurement program that, when executed by a computer, causes thecomputer to function as: a plurality of AD converters that respectivelyconvert analog detection signals output by a plurality of magneticsensors into digital measurement data, the plurality of magnetic sensorsbeing in a magnetic sensor array having a plurality of magnetic sensorcells capable of detecting magnetic fields in three axial directionsarranged in three dimensions, each magnetic sensor cell including aplurality of the magnetic sensors that each have a magnetoresistiveelement and a magnetic flux concentrator arranged at least at one of oneend and another end of the magnetoresistive element; a magnetic fieldacquiring section that acquires the digital measurement data; acalibration computing section that calibrates the digital measurementdata from the magnetic field acquiring section, using at least one of amain-axis sensitivity, cross-axis sensitivities, and an offset; and agradient magnetic field computing section that calculates a gradientmagnetic field using magnetic field measurement data resulting from thecalibration of the digital measurement data, and also calculates thegradient magnetic field in three dimensions for magnetic fields in allthree axial directions, by calculating a difference in magnetic fieldsbetween adjacent magnetic sensor cells among the plurality of magneticsensor cells, using the magnetic field measurement data measured betweenthe adjacent magnetic sensor cells.